Question

In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 20.4 and a standard deviation of 6.5.

Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18.

Answer 1

The probability of a randomly selected student scoring less than 18 on the reading portion of the test can be found by calculating the z-score and then using a normal distribution table or statistical software to find the associated probability.

Step-by-step explanation:

To find the probability that a randomly selected student scored less than 18 on the reading portion of the test, we first need to calculate the z-score which standardizes the student's score within the context of the given mean and standard deviation. The formula for the z-score is:

Z = (X - μ) / σ

Where X is the score in question (18), μ is the mean (20.4), and σ is the standard deviation (6.5). Plugging these values into the formula, we get:

Z = (18 - 20.4) / 6.5 = -0.3692

Next, we would use a normal distribution table or a statistical software to find the probability that corresponds to this z-score, which will give us the cumulative probability of selecting a student with a score less than 18. This probability is expressed as P(X < x).

Since this is a high school level mathematics question, specifically involving concepts from a statistics class, it is important to show step-by-step calculation to make sure the student understands the process.